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<div class="subTitle">org.apache.commons.math3.special</div>
<h2 title="Class Erf" class="title">Class Erf</h2>
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<pre>public class <span class="strong">Erf</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">This is a utility class that provides computation methods related to the
 error functions.</div>
<dl><dt><span class="strong">Version:</span></dt>
  <dd>$Id: Erf.java 1538368 2013-11-03 13:57:37Z erans $</dd></dl>
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<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erf(double)">erf</a></strong>(double&nbsp;x)</code>
<div class="block">Returns the error function.</div>
</td>
</tr>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erf(double, double)">erf</a></strong>(double&nbsp;x1,
   double&nbsp;x2)</code>
<div class="block">Returns the difference between erf(x1) and erf(x2).</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erfc(double)">erfc</a></strong>(double&nbsp;x)</code>
<div class="block">Returns the complementary error function.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erfcInv(double)">erfcInv</a></strong>(double&nbsp;x)</code>
<div class="block">Returns the inverse erfc.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/special/Erf.html#erfInv(double)">erfInv</a></strong>(double&nbsp;x)</code>
<div class="block">Returns the inverse erf.</div>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>erf</h4>
<pre>public static&nbsp;double&nbsp;erf(double&nbsp;x)</pre>
<div class="block">Returns the error function.

 <p>erf(x) = 2/&radic;&pi; <sub>0</sub>&int;<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p>

 <p>This implementation computes erf(x) using the
 <a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double, double, int)"><code>regularized gamma function</code></a>,
 following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p>

 <p>The value returned is always between -1 and 1 (inclusive).
 If <code>abs(x) &gt; 40</code>, then <code>erf(x)</code> is indistinguishable from
 either 1 or -1 as a double, so the appropriate extreme value is returned.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the error function erf(x)</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the algorithm fails to converge.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double, double, int)"><code>Gamma.regularizedGammaP(double, double, double, int)</code></a></dd></dl>
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<h4>erfc</h4>
<pre>public static&nbsp;double&nbsp;erfc(double&nbsp;x)</pre>
<div class="block">Returns the complementary error function.

 <p>erfc(x) = 2/&radic;&pi; <sub>x</sub>&int;<sup>&infin;</sup> e<sup>-t<sup>2</sup></sup>dt
 <br/>
    = 1 - <a href="../../../../../org/apache/commons/math3/special/Erf.html#erf(double)"><code>erf(x)</code></a> </p>

 <p>This implementation computes erfc(x) using the
 <a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaQ(double, double, double, int)"><code>regularized gamma function</code></a>,
 following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p>

 <p>The value returned is always between 0 and 2 (inclusive).
 If <code>abs(x) &gt; 40</code>, then <code>erf(x)</code> is indistinguishable from
 either 0 or 2 as a double, so the appropriate extreme value is returned.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value</dd>
<dt><span class="strong">Returns:</span></dt><dd>the complementary error function erfc(x)</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the algorithm fails to converge.</dd><dt><span class="strong">Since:</span></dt>
  <dd>2.2</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaQ(double, double, double, int)"><code>Gamma.regularizedGammaQ(double, double, double, int)</code></a></dd></dl>
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<h4>erf</h4>
<pre>public static&nbsp;double&nbsp;erf(double&nbsp;x1,
         double&nbsp;x2)</pre>
<div class="block">Returns the difference between erf(x1) and erf(x2).

 The implementation uses either erf(double) or erfc(double)
 depending on which provides the most precise result.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x1</code> - the first value</dd><dd><code>x2</code> - the second value</dd>
<dt><span class="strong">Returns:</span></dt><dd>erf(x2) - erf(x1)</dd></dl>
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<h4>erfInv</h4>
<pre>public static&nbsp;double&nbsp;erfInv(double&nbsp;x)</pre>
<div class="block">Returns the inverse erf.
 <p>
 This implementation is described in the paper:
 <a href="http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf">Approximating
 the erfinv function</a> by Mike Giles, Oxford-Man Institute of Quantitative Finance,
 which was published in GPU Computing Gems, volume 2, 2010.
 The source code is available <a href="http://gpucomputing.net/?q=node/1828">here</a>.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value</dd>
<dt><span class="strong">Returns:</span></dt><dd>t such that x = erf(t)</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.2</dd></dl>
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<h4>erfcInv</h4>
<pre>public static&nbsp;double&nbsp;erfcInv(double&nbsp;x)</pre>
<div class="block">Returns the inverse erfc.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the value</dd>
<dt><span class="strong">Returns:</span></dt><dd>t such that x = erfc(t)</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.2</dd></dl>
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